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If U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, and B = { 2, 4, 6, 8 }, then the number of elements in the set BтА▓ is:
5
9
8
4
5
Just count the elements in U and subtract the number of elements present in B; the number of even digits between 1-9 is exactly 4.
Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and set B = {2, 4, 6, 8}.
n(BтА▓)=n(U)тИТn(B)
Just count the elements in U and subtract the number of elements present in B; the number of even digits between 1-9 is exactly 4.
Students often miscalculate the total number of elements in U as 8 instead of 9 or include 0 which is not in the set.
Identify cardinality of sets
Determine the number of elements in the universal set U and subset B. Here, n(U)=9 and n(B)=4.
n(U)=9,n(B)=4
Apply complement definition
The set BтА▓ (complement of B) consists of all elements in U that are not in B. The number of elements is given by the difference of their cardinalities.
n(BтА▓)=9тИТ4
Final Calculation
Subtract the count of set B from the count of set U to get the final result.
n(BтА▓)=5
A is correct because the complement set BтА▓=1,3,5,7,9, which contains exactly 5 elements.
This concept is fundamental to Probability theory, where the probability of an event not occurring is calculated as P(AтА▓)=1тИТP(A).